Appendix: Multimodal Omics Data Integration Using Max Relevance-Max Significance Criterion

This paper presents a novel supervised regularized canonical correlation analysis, termed as CuRSaR, to extract relevant and significant features from multimodal high dimensional omics data sets [1]. The proposed method extracts a new set of features from two multidimensional data sets by maximizing the relevance of extracted features with respect to sample categories and significance among them. It integrates judiciously the merits of regularized canonical correlation analysis (RCCA) and rough hypercuboid approach. An analytical formulation, based on spectral decomposition, is introduced to establish the relation between canonical correlation analysis (CCA) and RCCA. It makes the computational complexity of the proposed algorithm significantly lower than existing methods. The concept of hypercuboid equivalence partition matrix of rough hypercuboid is used to compute both relevance and significance of a feature. The equivalence partition matrix also offers an efficient way to find optimum regularization parameters employed in CCA. The superiority of the proposed algorithm over other existing methods, in terms of computational complexity and classification accuracy, is established extensively on real life data.